PIRSA:24090178 Other Condensed Matter

Series: Quantum Matter

Barnett, J. (2024). Non-Hermitian operators in many-body physics. Perimeter Institute. https://pirsa.org/24090178

Barnett, Jacob. Non-Hermitian operators in many-body physics. Perimeter Institute, Sep. 17, 2024, https://pirsa.org/24090178 

@misc{ pirsa_PIRSA:24090178,
  doi = {},
  url = {https://pirsa.org/24090178},
  author = {Barnett, Jacob},
  keywords = {Condensed Matter},
  language = {en},
  title = {Non-Hermitian operators in many-body physics},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {sep},
  note = {PIRSA:24090178 see, \url{https://pirsa.org}}
}

Abstract

Non-Hermitian Hamiltonians are a compulsory aspect of the linear dynamical systems that model many physical phenomena, such as those in electrical circuits, open quantum systems, and optics. Additionally, a representation of the quantum theory of closed systems with non-Hermitian observables possessing unbroken PT-symmetry is well-defined.
 
In this talk, I will second-quantize non-Hermitian quantum theories with paraFermionic statistics. To do this, I will introduce an efficient method to find conserved quantities when the Hamiltonian is free or translationally invariant. Using a specific non-Hermitian perturbation of the Su-Schrieffer-Heeger (SSH ) model, a prototypical topological insulator, I examine how PT-symmetry breaking occurs at the topological phase transition. Finally, I show that although finite-dimensional PT-symmetric quantum theories generalize the tensor product model of locality, they never permit Bell inequality violations beyond what is possible in the Hermitian quantum tensor product model.

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